Sheikh Mohammed bin Abdulrahman Al Thani, speaking at the news conference in the Italian capital Rome on Saturday, said the list "was meant to be rejected", pointing to the fact that it arrived with a 10-day expiration date.
"Everyone is aware that these demands are meant to infringe the sovereignty of the state of Qatar, shut the freedom of speech and impose auditing and probation mechanism for Qatar," he said.
"We believe that the world is not governed by ultimatums, we believe that the world is governed by the international law, it is governed by an order that does not allow large countries to bully small countries."
Sheikh Mohammed spoke less than 48 hours before the deadline for the demands issued last week was due to pass.
It was not clear what would come next. Sheikh Mohammed said Qatar did not fear any military retaliation for rejecting the ultimatum.
The list of demands includes downgrading ties with Iran, shutting down Al Jazeera Media Network and Turkish military base in Doha.
The ultimatum came more than two weeks after Saudi Arabia, the United Arab Emirates, Bahrain and Egypt cut diplomatic ties with Qatar on June 5 and imposed sanctions, accusing it of supporting "terrorism".
Sheikh Mohammed said on Saturday that "those parties brand any party of state who opposes their designs as terrorists."
He also said that Trump was manipulated into believing that Qatar was not doing enough to crack down on funding "extremists".
"The United States administration and institutions firmly believe in the state of Qatar, yet the statement made by President Trump was based on false allegations and the false impression given to him by the heads of states who imposed a blockade on Qatar," he said.
Trump would be able to find "the true, established facts" from the US institutions, according to Sheikh Mohammed.
"The state of Qatar has been subjected to unlawful measures on the basis of false allegations without the submission of evidence," he said.